期刊
ADVANCES IN MATHEMATICS
卷 223, 期 1, 页码 49-97出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2009.07.005
关键词
Asymptotics; Wave equation; de Sitter space; Scattering operator; Fourier integral operator
类别
资金
- National Science Foundation [DMS-0201092, DMS-0733485, DMS-0801226]
- Clay Research Fellowship
- Sloan Fellowship
In this paper we obtain the asymptotic behavior of solutions of the Klein-Gordon equation on Lorentzian manifolds (X degrees, g) which are de Sitter-like at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces. Under global assumptions on the (null)bicharacteristic flow, namely that the boundary of the compactification X is a union of two disjoint manifolds, Y(+/-) and each bicharacteristic converges to one of these two manifolds as the parameter along the bicharacteristic goes to +infinity, and to the other manifold as the parameter goes to -infinity, we also define the scattering operator, and show that it is a Fourier integral operator associated to the bicharacteristic flow from Y(+) to Y(-) (C) 2009 Elsevier Inc. All rights reserved.
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